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If two Pokemon have the same speed, and are not holding Quick Claw, then it's random (50/50) who goes first.

Quick Claw gives the holder a 20% chance of moving first.
If it doesn't activate for either Pokemon, then the first mover will be random as above.
If it activates for both Pokemon, then the first mover will be random as above.
If it activates for one of the Pokemon and not the other, that Pokemon will move first.

Here's some fun maths, if you're interested. There is an 80% chance for each Pokemon that it won't activate, so a 64% chance (0.80.8) it will not activate for both Pokemon. And a 4% chance (0.20.2) it will activate for both Pokemon. Therefore: